A051463 Molien series for group G_{1,3}^{8} of order 4608.

1, 1, 37, 229, 721, 2152, 5083, 10167, 19637, 34575, 56511, 90552, 138093, 201909, 291549, 408225, 556325, 751696, 994583, 1291355, 1666301, 2117627, 2654051, 3310736, 4082489, 4980745, 6054261, 7292797, 8710873, 10373848, 12264499, 14400799, 16868005, 19639687

Offset

0,3

Links

Table of n, a(n) for n=0..33.

E. Bannai, S. T. Dougherty, M. Harada and M. Oura, Type II Codes, Even Unimodular Lattices and Invariant Rings, IEEE Trans. Information Theory, Volume 45, Number 4, 1999, 1194-1205.

Index entries for linear recurrences with constant coefficients, signature (2, -1, 4, -8, 4, -6, 12, -6, 4, -8, 4, -1, 2, -1).

Index entries for Molien series

Formula

G.f.: (5*x^12 + 51*x^11 + 190*x^10 + 400*x^9 + 846*x^8 + 947*x^7 + 882*x^6 + 795*x^5 + 304*x^4 + 152*x^3 + 36*x^2 - x + 1)/((x - 1)^6*(x^2 + x + 1)^4).

a(n) ~ 64*n^5/135. - Stefano Spezia, Aug 21 2022

Mathematica

CoefficientList[Series[(5x^12+51x^11+190x^10+400x^9+846x^8+947x^7+882x^6+795x^5+304x^4+152x^3+36x^2-x+1)/((x-1)^6(x^2+x+1)^4), {x, 0, 40}], x] (* or *) LinearRecurrence[ {2, -1, 4, -8, 4, -6, 12, -6, 4, -8, 4, -1, 2, -1}, {1, 1, 37, 229, 721, 2152, 5083, 10167, 19637, 34575, 56511, 90552, 138093, 201909}, 40] (* Harvey P. Dale, Jul 14 2021 *)

Crossrefs

Cf. A051461, A051462.

Sequence in context: A284987 A133958 A088544 * A275750 A142445 A155974

Adjacent sequences: A051460 A051461 A051462 * A051464 A051465 A051466

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jun 15 2001

Status

approved